The present invention relates to orbit transfer techniques, and more particularly to systems and methods for efficiently transferring a spacecraft from one orbit to another orbit.
Typically, a spacecraft is launched into an initial orbit that differs from the final orbit that the spacecraft is to follow during its lifetime. A spacecraft launch vehicle places the spacecraft in its initial or launch vehicle insertion orbit. The launch vehicle, however, generally does not have sufficient capability to place the spacecraft into its mission orbit. As a result, the spacecraft must be transferred from its initial insertion orbit to its final mission orbit, typically by using a spacecraft on-board propulsion system.
For a geosynchronous orbit (GEO) spacecraft, a velocity change (Delta-V) of approximately 1600 m/sec is needed to transfer the spacecraft from a typical injection orbit to a final GEO orbit. As one skilled in the art will appreciate, the time allocated to transfer the spacecraft to the final mission orbit is limited, so the spacecraft typically requires a high-thrust propulsion system to generate the needed velocity change for a large spacecraft dry mass (e.g., 2000 to 3500 kg).
The high-thrust propulsion system can comprise a liquid apogee engine (LAE) that burns a mixture of hydrazine and oxidizer to generate a thrust of about 100 to 150 lbf with a mass specific impulse (ISP) of about 325 seconds (the ISP is the ratio of the thrust to the mass flow rate, a higher value indicating that less fuel is needed to achieve the same applied impulse). The orbit transfer then can be performed by performing a sequence of four to six LAE maneuvers at or near the orbit apogee, with each maneuver lasting less than 1 hour. Using this approach, the transfer to the GEO mission orbit can be accomplished in less than 2 weeks. However, the performance of this approach, as measured by the mass delivered to orbit on a given launch vehicle, is limited by the capability of the launch vehicle and the amount of chemical propellant that can be stored on-board the spacecraft.
The LAE orbit transfer approach provides reasonable efficiency and a rapid orbit transfer, but for heavy spacecraft the combined launch vehicle and on-board LAE system can be insufficient to transfer the spacecraft to the mission GEO orbit. To address this problem, a hybrid orbit transfer approach recently has been introduced that performs the orbit transfer in two phases. The first phase includes some number of LAE firings to transfer the spacecraft from the initial injection orbit to an intermediate orbit, which typically has its perigee above the Van Allen radiation belts to limit solar array degradation during the final orbit transfer phase (phase 2).
During phase 2, high-efficiency low-thrust thrusters, such as ion thrusters, are fired for a period of several weeks to several months to complete the transfer to the mission GEO orbit. The thrusters can be gridded ion thrusters or Hall Current Thrusters (HCTs), which generate thrust by ionizing xenon atoms and accelerating them through a potential gradient. The ion thrusters have low thrust (e.g., less than 0.1 lbf), but have high specific impulse of from about 2000 to about 3500 seconds. Because this phase uses low thrust thrusters, the thrusters must be fired for extended time periods to provide a significant benefit.
The time available to perform the final orbit transfer phase (phase 2) depends on the orbit time that is acceptable to the customer. Because the customer almost always wants revenue generating service to begin as soon as possible after the spacecraft launch, the allocated time usually is not more than 90 days. The longer the allocated time, the longer the ion thrusters can fire, and therefore, the larger the achievable payload mass that can be delivered to the mission orbit.
According to prior-art implementations of the above described orbit transfer approach, the ion thrusters are fired continuously while the spacecraft attitude is controlled so that the thrust vector follows a pre-specified inertial trajectory, referred to as a thrust vector trajectory. This approach is referred to as a continuous firing strategy. The thrust vector trajectory can be determined by numerical optimization techniques well known to those skilled in the art. For example, the continuous firing thrust vector trajectory can be calculated to provide a transfer from an initial orbit to a final orbit in the minimum possible time. The resulting minimum-time transfer-orbit trajectory consists of a specific time history of the orbit elements as they vary from an initial orbit to a final orbit while the thrusters are firing continuously. With this strategy, continuous thruster firing typically is maintained, except in locations where it is not possible, for example, due to the lack of adequate electrical power during eclipse periods, or due to unanticipated failures and contingencies.
The drawback of the continuous firing strategy is that, for at least some portions of the orbit, the thruster firing is inefficient. For example, inefficiencies may occur when the intermediate orbit (final phase start orbit) has an apogee altitude equal to the GEO altitude (synchronous altitude) and has zero inclination. In this case, there is no useful benefit for the thrust provided in the region around orbit perigee, since thrusting at perigee is most useful for changing the apogee altitude or inclination, and neither of these corrections are required in this case.
To provide a higher efficiency orbit transfer, alternative strategies are possible where the thrusters are fired for only a portion of each orbit, in regions where firing is most efficient. This approach is referred to as an on/off firing strategy. For example, it is well known that, in the above example of an orbit with a synchronous altitude apogee, the thrusters may be fired efficiently for some region about apogee to correct inclination and raise the perigee altitude. One drawback of this approach, however, is that although the efficiency of firing can be increased, the firing can be sufficiently intermittent so that it is not possible to deliver the spacecraft mass to GEO orbit within the allocated time.
Furthermore, current on/off firing strategies tend to be “ad hoc”. That is, the off and on firing regions are selected based on experience with impulsive maneuvers, such as LAE maneuvers, and preferred orbital regions for executing such maneuvers. Additionally, the functional form of the expression used to model the thrust vector trajectory also may be determined based on experience. The trajectory itself may then be determined using a numerical optimization procedure in which the trajectory model parameters are varied to achieve the best results. The use of an assumed thrust vector trajectory and ad hoc selected orbital firing regions imposes artificial constraints that limit the performance of these methods compared to methods where the optimal trajectory and on/off firing regions are solved for directly.
Thus, an improved method is desired that may be used to determine thrust trajectory and on/off firing regions in a way that provides a fuel use reduction with minimum impact to the total orbit transfer time. Preferably, the method does not require the use of assumptions regarding the functional form of the thrust trajectory or the orbital locations where firing should occur. Also, a system is desired for implementing such a trajectory and firing regions on-board a spacecraft to perform a transfer from an intermediate orbit to a final mission orbit.